A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate 2 feet per second. 25 ft sec (a) What is the velocity of the top of the ladder when the base is given below? 15 feet away from the wall ft/sec -1.5 20 feet away from the wall -8/3 ft/sec 24 feet away from the wall -48/7 ft/sec (b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area o the triangle is changing when the base of the ladder is 24 feet from the wall. -17 X ft?/sec (c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 24 feet from the wall. 0.00232 X rad/sec
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate 2 feet per second. 25 ft sec (a) What is the velocity of the top of the ladder when the base is given below? 15 feet away from the wall ft/sec -1.5 20 feet away from the wall -8/3 ft/sec 24 feet away from the wall -48/7 ft/sec (b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area o the triangle is changing when the base of the ladder is 24 feet from the wall. -17 X ft?/sec (c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 24 feet from the wall. 0.00232 X rad/sec
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Transcribed Image Text:A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of
2 feet per second.
(a) What is the velocity of the top of the ladder when the base is given below?
15 feet away from the wall
-1.5
V ft/sec
20 feet away from the wall
-8/3
V ft/sec
24 feet away from the wall
-48/7
v ft/sec
(b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of
the triangle is changing when the base of the ladder is 24 feet from the wall.
-17
X ft?/sec
(c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the
ladder is 24 feet from the wall.
0.00232
X rad/sec
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